This figure is not drawn to scale. A rectangular glass tank 85 cm by 59 cm by 43 cm has 2 compartments, B and C, with a water height of 31 cm in B and 10 cm in C. A hole in the slider caused water to leak from B to C. It was found that the water level in both compartments became the same after some time.
- What is the height of water in the tank now?
- It took 114 h for the water in both compartments to reach the same level. Assuming that water leaked at a constant rate, how much water flowed from B to C in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment B
= 34 x 31 x 59
= 62186 cm
3 Length of Compartment C
= 85 - 34
= 51 cm
Volume of the water in Compartment C
= 51 x 59 x 10
= 30090 cm
3 Total volume of water
= 62186 + 30090
= 92276 cm
3 Base area of the glass tank
= 85 x 59
= 5015 cm
2 Height of water
= 92276 ÷ 5015
= 18.4 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment B
= 31 - 18.4
= 12.6 cm
Drop in the volume of Compartment B
= 59 x 34 x 12.6
= 25275.6 cm
3 Volume of water flowed from B to C in 1 minute
= 25275.6 ÷ 75
≈ 337 cm
3 Answer(s): (a) 18.4 cm; (b) 337 cm
3